PDF Modelling of Reinforced Concrete. Beam for Flexural Behaviour

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MODELLING OF REINFORCED CONCRETE. BEAM FOR FLEXURAL BEHAVIOUR

Lydia Kristen Binti Edward Mongudal

Bachelor of Engineering

with

Honours

'fA ₆₈₃_.₂

(Civil Engineering)

L983 2005

2005

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NIVERSITI MALAYSIA SARAWAK BORANG PENYERAIIAN STATUS TESIS

Judul: ____________~~~·I~o~d~e~ll~in~g~o=f~R~e~in~f~o rc~~~~o~n~c~r~e~te~B~e~~c(1 C ~a~n~l____________

for Flexural Behaviour Sesi Pengajian: 7004 - 2005

Saya LYDIA KRISTEN BINTI EDWARD MONGUDAL (HURUF BESAR)

rnengaku rnernbenarkan le~is * loi disimpan di Pusat Khidmat Maklumat Akademik, Universill Malaysia Sarawak dengan syaral-syarat kegunaan seperli berikut:

1. Tesis adalah hakrnilik Universili Malaysia Sarawak.

2. Pusal Khidmal Maklumal Akademik, UOIversili Malaysia Sarawak dibenarkan membU<.I l salinan umuk IUJuan pengaJlan sahaja.

3. Membual pendigitan unwk membangunkan Pangkalan Data Kandungan Telnpalan.

'-L Pusat Khidmat maklumat Akademik, Cniversio Malaysia Sarawak dlbenarkan meUlbu3t sallnan Il;!sis Uti

sebagai bahan pertukaran antara institusi pengajian tinggi.

5. ** Sib tandakan ( .j) di kotak berkeuaan

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^SULIT ^(Mengandungi maklumat yang berdarjah keselamatan atau kcpenftogan Malaysia seperti yang termaktub di dalam AKTA RAHSIA RASM I 1972)

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^TERHAD (Mengandungl maklumat TERHAD yang telah di1entukan u!eh organisastlbadan di mana penyelidlkan dJjaJankan).

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TIDAK TERRAD

Disahkan oleh:

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(TANDATANGAN p. ULlS) (TANDATANGAN PI:N e LlA)

ALAJ\1AT TETAP: ₍ J •

P.O. Box 125,

Kg. T ingkalanon, Nama Penyelia

Kota Marudu, Sabah. Malaysia.

Tarikh: I

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CAT.\TAN • Tesis di,,'aksudk;ln s{'bagai 1c.~L~ b)lgi Ijal.ah Ool.lO~ F,)I~afah. Sarjana dan Sll~jana .\ lulla

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dt'ngan men)'tuakan ~ck"li ~dJab dan It''''p" h lI~is ini perl" dil.d"$k:1n l>\"ba:!.ai Sl LIT dan n:RIL-\O.

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This final year project attached here;

Title : Modelling of Reinforced Concrete Beam for Flexural Behaviour Author-s name: Lydia Kristen Binti Edward Mongudal

Matrix number: 6765

Has been read and app roved by

•

^Prof.^Ma^{d ya.}^{Dr. N}^g^Chee^KJlOoⁿ ^Da^te

Supervisor

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MODELLING OF REINFORCED CO 'CRETE BE M FOR FLEXURAL BEHAVIOUR

P_KHIDMAT MAKlUMAT AKAOEMIK UN 1M AS

1l1li11111111111111111111111

1000143629

LYDIA KRISTEN BlNTI EDW RD 1\10 GUDAL

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This Report is Submitted to Faculty of Engineering, Univcrsili Malaysia Sarawak ill Partial Fulfillment of tbe Requirements for the Degree of

Bachelor of Engineering with lIonours (Civil Engineering) ZOOS

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Dedicated to beloved Mom amI Dad, Roy, EVil, Beeea and Ronn.

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I

ACKNOWLED GEMENT

Thank GOD for giving me enough time, strengthen me in pain, inspiring and guiding me throughout the completion of this project. For without Him, it is impossible for me to complete this project on time thus successful.

Having this opportunity, I would like to express my highly gratitude to my supervisor, Prof. Madya. Dr. Ng Chee Kboon for the advise, guide and support in order for me to produced a quality report.

Special thanks goes to my beloved mom and dad for their unceasing love, prayer, and financial supports. To my dearly brothers, sisters, relatives, course mate, and friends, I thank God once again for giving me a lovely person like you all. To Miss. Esther Sanggedha Anandaraj, thanks for the guide, prayer, and support in time of need.

I wish ftnally to express my deep appreciation to all the Faculty of Engineeling lecturers, staffs, technicians, especially Mr. Rhyier Juen for allowing me using CATIA Lab in finishing my FORTRAN program.

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ABSTRACT

A FORTRAN program for the non-linear analysis of reinforced concrete beam has been developed in this study. This program is able to produce the complete load-deflection behaviour and moment-curvature relationship for the whole flexural response of the beams. The computational results have been verified by manual calculations, indicating that any error in the calculation has been avoided. However, this program is only applicable to simply-supported T

beams with both compression and tension reinforcements.

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ABSTRAK

Satu program FOTRAN bagi analisa ketidak linearan rasuk konkrit bertetulang telah dibina dalam kajian ini. Program ini mampu menghasilkan tindakan beban-pemesongan dan hubungan daya-kelengkungan yang lengkap bagi kesemua respons kclentumn rasuk tersebut. Hasil pengiraan telah disahkan melalui pengiraan manual, menunjukkan sebarang kesilapan dalam kiraan telail dielakkan. Walaubagaimanapun, program ini hanya boleh digunakan unruk rasuk

T sokongan-mudah bersama kedua-dua tetulang kemampatan dan ketegangan.

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3.4 FORTRAN Program Design 22

CHAPTER 4 RESULTS '001 USSlO.:'lS

4.1 Beam Model

4.2 Manual Computations

28

4.2.1 Computation for Uncracked Section

4.2.2 Computation for Cracked Section

35

4.3 Comparison between Manual and FORTRAN

Computations Results. 43

4.4 Moment Vs. Curvature 43

4.5 Load-Deflection Behavior 46

VII

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CHAPTER S CONCLUSIONS AI'lD RECOMMENDATIONS

5.1 Conclusions 49

5.2 Recommendations 50

REFERENCES 51

APJ)ENDIX: FORTRAN PROGRAM LlSTI G 52

VIIl

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LIST O F TABLES

Table Page

Partial list of programming languages interest to engineers 7

2 Manual computation results for the total of initial force and 42 initial moment for C₁= 96.63Rmm

3 Comparison for manual and FORTRAN results

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LIST OF FIGURES

Figure Page

Load-deflection behaviour of a reinforced concrete beam 10

symmetrically pl.aced concentrated loads

H The Top-down design process ^7'

2 Moment-curvature diagram for a reinforced concrete beam 11

3 Strain and stre s distribution of an uncracked beam section 15 4 Strain and stress distribution of a cracked beam section 18 5 Division of segment in the parabolic stress block 18 6 Load-deformation relationship of a beam under two 21

7 Load-midspan deflection of a reinforced concrete beam ~1 _J

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Flowchart of the FORTRAN program for the beam 25 anal ysis

10 Beam dimensions and reinforcement details

29

1 I Distribution of strains and stresses in cracked beam section 36

I~ Uncracked beam in the elastic range ofloading 43

13 Moment-curvature diagram 47

[4 Load-deflection diagram 48

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LIST OF NOTATIONS

area of nonpreslressed tension reinforcement area of compression reinforcement

flange width B,.\. web width

Cc concrete compressive force in cross section Cs steel compressive force in cross section

C/ distance from extreme compression fiber to neutral axis

Ds effective depth, that is, distance from extreme compression fiber to centroid of tension reinforcement

D's distance from extreme compression fiber to centroid of compression reinforcement

Ec modulus of elasticity of concrete Es modulus of elasticity of reinforcement 1-1 overall thickness of member

HF flange thickness Fn the initial force

let splitting tensile strength of concrete feu specified compressive strength of concrete

(i modulus of rupture of concrete

Is

^calculated stress in reinforcement at service loads

Xi

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/Y Ie

Ie)'

Ie h e

Ig

Igt

LAM

LB

,Ha ,ller Mn n P YB

Y

_c

Y_ue

specified yield strength of non prestressed reinforcement cylinder compressive strength of concrete

moment if inertia of cracked section transfonned to concrete effective moment ofincrtia for computation of deflection

the effective moment of inertia for computation of deflection of cracked T-section

the effective moment ofineltia for computation of deflection of uncracked T -section

moment of inertia of gross concretc section, neglecting reinforcement

moment of inertia of gross transfomled uncracked section the lever ann of the compression force from top fibre the centre o f level of each secti on

applied moment in member cracking moment

the initial moment modular ratio tbe axial load

the level of each section

the centroid for cracked transfonn of doubly reinforced T-section the distance from centroid to extreme fiber of the transfonned section

distance from the centroidal axis to the extreme fibre in tension

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distance from the centroidal axis to the extreme fibre in compression

Cc the strain in concrete E'cl the strain

Cs the strain in steel

(/J the curvature of each cross section

f./)c the curvature for cracked T-section

(/)"c the curvature for uncracked T-section

de

the deflection for cracked T-section

Auc the deflection for uncracked T-section L:Fn total of the initial force

L:Mn total of the initial moment

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CHAPTER 1 IN TROD U CTION

1.1 General

Beam is one of the most common elements in design of reinforced concrete.

Concrete beam in nature has a character which is strong in compression and weak in tension. In order to resist the tension, embedded materials, usually in the form steel bars, are provided in the concrete beam. Such combination create reinforced concrete beam. Reinforced concrete beam has the ability to rcsist both compressive and tensile stresses. If a reinforced concrete beam is designed properly, it can perform well to resist the bending moment due to subjected load applied to the member. Thus, it is essential to study the load-deformation response of a reinforced concrete beam to provide the designer the principles required to apply in the design consideration.

1.2 Ilistorical Developmenl IIf Reinforced Concrete

Reinforced concrete has been used as building material since last decades

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and still preferable nowadays. It is widely used in most countries because of the wide availability of reinforcing bars and economy of concrete constituents such as cement, aggregate and water.

In 1801, Frenchman, F. Coignet has published his statement of principles of construction, recognising the weakness of concrete in tension. He then, published a book illustrating the uses of reinforced concrete in 1861. For the first time, in 1848, another Frenchman, J.L. Lambot construct a rowboat of concrete reinforced with wire for exhibition in the 1855 World's Fair in Paris. His model included drawings of a reinforced concrete beam and a column reinforced with four round iron bars (MacGregor, 1992).

In 1850s, an American lawyer and engineer, Thaddeus Hyatt has carried out an experiment of reinforced concrete beams. He provides longitudinal bars in tension zone and vertical stirrups for shear in his beams. Unfortunately, Hyatt's work was not known until he privately published a book describing his tests and building system in I 877(MacGregor, 1992).

In 1867, J. Monier, owner of French nursery garden, has patented concrete containers reinforced with metal frames for planting trees. His same patent then was used to patent another reinforced concrete structure such as reinforced pipes and tanks (1868), flat plates (1869), bridges (1873), and stairs (1875) (MacGregor,

1992).

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Professors Morsch and Bach of the University Of Stuttgart has carried out an experiment to test the strength of reinforced concrete and the method of computing the strength of reinforced concrete was developed Mr. Koenen, chief building inspector for Prussia. He published the first manuscript on the theory and design of concrete structures in 1886. In his book, he presented an analysis which assumed that the neutral axIS was at the midheight of the member (MacGregor,

1992)

W.E. Ward, a mechanical engineer built the first reinforced concrete building in the United States in I :::~:;. It was a house built on Long Island. In 1988, E.L.

Ransome constructed a building having cast-iron columns and a reinforced concrete floor system consisting beams and slab made from flat metal arches covered with concrete. In 1890, Ransome built the Leland Stanford, Jr. Museum in San Francisco. This two-story building used discarded cable car rope as beam reinforcement. In 1903, he built the fLrst building in the United States completely framed with reinforced concrete in Pennsylvania. In 1906, C.A.P. Turner developed the first flat slab without beams (MacGregor, 1992).

In the last two decades, many books, technical ar1icles, and codes present the theories of mechanical behaviour of reinforced concrete and help the engineer came to understand the principles applied in design procedures. As in 1894, Coignet (son of the earlier Coignet) and de Tedeskko extended Koenen's theories to develop the working stress design method for flexure (MacGregor, 1992).

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1.3 Problem Statement

Understanding on the behaviour of the reinforced concrete beams has become more important as it is a basis of ideas for designing a reinforced concrete member Before proceeding to design process, a section should be analyzed to determine if its nominal resisting strength is adequate to carry the load applied to the member. However, because of a large numbers of parameters that should be considered in analysis, such as geometrical width, depth, area of reinforcement, steel strain, concrete strain, steel stress, and so on, computer programs arc required to assist the analysis.

This project studies on the flexural behaviour of reinforced concrete beam with a computer model based on section analysis. Non-linear behaviour of materials are seldom considered in computer models, but it will be considered in this stud y.

1.4 ;\ i m and Objectives

The main aim of this project is to model the flexural behaviour of reinforced concrete beams. Development of this model is made using Fortran 90 program. The flexural resistance will be calculated by using cross section analysi" based on force equilibrium and compatibility. Deflection of the beam will be calculated by conjugate beam method based on curvature. Therefore, the load-deflection

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response is obtained. All calculation will be based on ACI Building Code (1999).

1.5 Chapter Overview

This project is divided into two parts. The first part consists of three chapters.

Chapter I gives a brief introduction of reinforced concrete beam. Historical development of reinforced concrete, problem statement, aim and objectives, and chapter overviews are included. Chapter 2 presents computer programming background and reason argument about flexural behaviour of reinforced concrete beam. The method of analysis used in determining the flexural resistance and deflection are discussed in Chapter 3.

[n the second part of this project, Chapter 4 gives the case scenario and based on this, the data given will be used in Fortran computation to get the flexural response. After the completion of the computational program, the results both from manual and Fortran computations are discussed. Chapter 5 presents the conclusions indicating the achievement of the aim and objectives of this project and some recommendations for future use.

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CHAPTE R 2

LITERATURE RE VIEW

2.1 Computer Program and Engineering

20^th

The computer is the most important invention of the century. A computer is a special type of machine that stores infonnation and can perfonn mathematical calculations on that infonnation at speeds much faster than human beings can think (Mayo and Martin, 1991). A program, which is stored in the computer's memory, tells the computer what sequence of calculations are required and which infonnation to perfonn the calculations on.

Engineers and scientists were among the first large-scale computer users dating back to the earliest back of the invention of computers. Engineers use computers in many ways, but the software that they used 'Jsually falls into two broad categories. The first contains utilities, such as word processing and graphics programs, that are low-cost packages and require no programming. The second category includes programs devoted specifically to engineering applications. This requires that the engineers to write their own program. Sometimes it is possible to modify an existing program, but some programming is unavoidable. There

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are five major uses of computers in engineering such as modelling and simulations, data acquisition, data analysis, process control, and design.

There are various programming languages of interest to engineers. Table 2. 1 list some of the programming languages and its strong points (Mayo and Martin,

199 1).

Table 2.1: Partial list of programming languages of interest to engineers

I'rogrammlng Languages

Description

a) FORTRA~ A compiled language widely used for engineenng applications. Contains a ful l range of stnlctured commands and uses of subroutines which promote good style. Periodic revisions update the language to include new advances.

b) BASIC' An interpreted language primarily used for its simplicity. TI1e lack of stnlctured commands tends to produce the problematic spaghetti code. The stnlcture of a subroutine usmg the GOSUB statement prevents developmellt of long programs.

Proprietary dialects, such as QuickBAS IC eliminate so me of these problems.

c) Pascal A compiled language which utilizes stnlctured conSlnlcts.

Promotes good programming practice. Very good for handling non.llumen c data, but somewhat limited for computational work.

d) C Very powerful compiled language which combines ,;ystem level and high-level commands. Requires an advanced level of programming experience and can be somewhat difficult to debug. Debugging problems are most severe for lengthy programs.

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2.2 Application of FORTRAN Programming Lnnguagc In Ci\'il Engineering

Programming language has been used in Civil Engineering in a variety of application. Computer program such as ABAQUS, ANSR, and FEAP were written in the FORTRAN computer language for the structural analysis (Austin ct.

a!. 1995). These programs offered a restricted, but well implemented, set of numerical linear/nonlinear time-history response calculations.

The LSTRLP algorithm is implemented by an optimization code written in Fortran 90 (Lamberti and Pappalettere, 2003). The optimization code is tusted in eight cases of weight minimization of bar truss and frame structures. The Gauss

Legendre method was used for the numerical integration of each of the integrals.

The system of non-linear equatIOns (including contributions from all elements) was solved using FORTRAN. A good agreement between experimental and predicted data was obtained (Yamsaengsung and Moreira, 200 I). In 2004, ESOU 90002 introduces a FORTRAN program, provided in both compiled and uncompiled forms as ESOUpac A9002, for calculating the flexural buckling strength, and the local and inter-rivet buckling stresses. f uniform section SlruL~.

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